# Is there a statistical measure that combines difference in means and dispersion?

I am working on an academic physics problem, where I am trying to determine favourable variables in two data sets, where both data sets have the same variables.

The most favourable variables would have the highest difference in means and a small dispersion of data - a small 'spread'.

Is there a statistical measure/metric that combines both the difference in means and dispersion of data in this way?

• A standardised effect size like Cohen's d is probably what you want. en.wikiversity.org/wiki/Cohen%27s_d Mar 5, 2020 at 12:35
• This page on standardised effects has more discussion. en.wikipedia.org/wiki/… Mar 5, 2020 at 12:42
• And t-statistic (from two sample t.test) may fit your goal.
– Pere
Mar 5, 2020 at 12:57
• This is a valuation problem: one in which you must make a trade-off between an increased difference in means and a decrease in dispersion. Accepting some solution that has been used in other applications would amount to supposing your values are comparable to those of the other applications--which, even if plausible, ought to be checked. The most general solution will be of the form $\alpha f(m)-\beta g(d)$ where $f$ and $g$ are non-decreasing functions, $\alpha$ and $\beta$ are non-negative numbers, and $m$ is the mean difference and $d$ is some measurement of the dispersion.
– whuber
Mar 5, 2020 at 16:13
• (Continued) In light of this, what information can you add to your question that will help us understand, quantitatively, how you value these potential trade-offs?
– whuber
Mar 5, 2020 at 16:14

Standardised effect sizes scale the difference between groups by the variance within each group. Cohen's $$d$$ is probably the simplest and most widely used. Cohen's $$d$$ is also sometimes called the 'standardised mean difference'.